Photonic band gap materials are characterized by the property that they allow electromagnetic waves with a discrete set of frequencies to propagate, while blocking others. The allowed frequencies, as functions of the wave number, form the boundaries of the band gap and the size of the bandgap determines which frequencies are allowed to pass and which frequencies are rejected. Photonic band gaps can be exploited in many ways for practical applications. One such application is as a high-efficiency reflector for all directions and polarizations of photonic radiation (e.g. light, microwave, etc.).
Conventional microwave ovens operate at the ground state frequency radiation of 2.45 GHz. However, the source magnetron also generates radiation at other frequencies with varying intensity. Leakage of radiation is undesirable for health reasons. Most of this radiation is contained by conventional techniques, which are reasonably adequate for lower frequencies, but for higher frequencies suffer from inefficiency and design complications due to the higher penetration power of those frequencies. In addition to the health reasons, the fifth harmonic frequency of 12.25 GHz, which has a significant intensity, interferes with other household appliances (e.g.: phones, televisions) and with communication equipment in aircraft and satellites. For this reason, there has been substantial interest in developing better techniques to prevent this harmonic from leaking from microwave ovens.
There are generally two ways in which microwave energy is supplied to food within the cooking cavity of a microwave oven: by direct feeding to the cavity or via a waveguide. Most oven manufacturers prefer waveguide feeding for its ability to better distribute the energy to the food and for the added design flexibility provided by de-coupling the magnetron location from the cavity geometry. Shielding is employed in certain applications to prevent undesirable leakage of harmful radiation from the cavity. For example, screens are sometimes used in appropriate configurations to prevent radiation leakage. Such structures are satisfactory to block the radiation of lower frequencies, but for higher frequencies they are cumbersome. Because of the greater penetration power of high frequency radiation, shielding of the fifth harmonic requires screens covering most of the outer boundary of the cavity walls. It would therefore be desirable to reduce or eliminate the need for this type of shielding by blocking or suppressing emission of fifth harmonic frequencies from the magnetron itself using an appropriate waveguide mounted reflector device.
U.S. Pat. No. 6,130,780, filed Feb. 19, 1999 by Joannopoulos, et al., discloses an omnidirectional reflector made using a one-dimensional PBG crystal. The bandgap defines a range of frequencies that are reflected for electromagnetic energy incident upon the surface of the crystal. Use of the crystal as a radiation reflector in waveguide-fed microwave ovens or elsewhere is not disclosed.
Photonic bandgap crystals may also be used in the design of waveguides and splitters. The usual design method is based on the introduction of defects or deformities into PBG crystals. These defects may destroy the periodicity of the crystal; for example, in a straight wave guide, periodicity in one dimension is lost. Since the band structure is an outcome of the periodicity, the introduction of defects may alter the band structure in a drastic way. This renders the design process less flexible and subject to some trial and error experimentation.
U.S. Pat. No. 6,941,055, filed Nov. 30, 2004 by Segawa, et al., discloses a photonic bandgap waveguide wherein a defect region of incomplete crystal periodicity is used to guide an optical signal. This optical crystal is for a specific polar geometry and is not applicable as a frequency splitter. The crystal is not disclosed for any particular application and suffers from design complications as a result of the defect-based design methodology.
The simplest geometric configuration exhibiting the band gap property is a stack of dielectric slabs separated by layers of another dielectric. In designing a photonic bandgap reflector, the allowed bandgap frequencies are determined by the eigenvalues of a self-adjoint operator. A widely used algorithm to compute the eiegenvalues is to use the Rayleigh-Ritz method, as described in J. D. Joannopoulos, R. D. Meade and J. N. Winn, Photonic Crystals (Princeton University Press, Princeton, N.J., 1995, pp. 127-129), which is hereby incorporated herein by reference. This results in an approximation of the dielectric constant, which in this case is a discontinuous function, by a truncated Fourier series. Partial Fourier sums to discontinuous functions are known to suffer from the Gibbs phenomenon. They produce approximations with oscillations in the neighborhoods of the discontinuities, which do not diminish as the order of the approximation is increased. In the limit of infinitely many plane waves, the variation at each discontinuity does not converge to the jump. This property leads to poor convergence of the method, extending the required computational time and impeding accurate calculations to be performed that are critical for adequate understanding of the properties of the photonic band gap material. As a result, prior art design methods have provided limited accuracy at finite orders consistent with reasonable computational times. More accurate determination of bandgap boundaries therefore has required extended computational time, sometimes in the order of hours or days. Design difficulties arising from a lack of flexibility in this approach have limited the range of practical applications for real-world systems.
In order to design practical photonic bandgap reflector-suppressors, it would therefore be desirable to have a software tool that allows the calculations to be performed efficiently for a specified frequency, physical geometry and dielectric material at a finite order that delivers accurate bandgap boundaries within a reasonable computational time.
The need therefore exists for improved design concepts and design software that result in improved photonic bandgap reflectors, waveguides and splitters.